Former Connecticut Sen. Joe Lieberman gives a thumbs-up as he leaves the West Wing of the White House in Washington, Wednesday, May 17, 2017. The White House says President Donald Trump will be interviewing four potential candidates to lead the FBI.

Former Connecticut Sen. Joe Lieberman gives a thumbs-up as he leaves the West Wing of the White House in Washington, Wednesday, May 17, 2017. The White House says President Donald Trump will be interviewing four potential candidates to lead the FBI.

President Donald Trump said Thursday that he is "very close" to naming a new FBI director to replace the one he fired more than a week ago and that former Connecticut Sen. Joe Lieberman was among his top choices for the job.

Lieberman was among four candidates Trump interviewed at the White House on Wednesday.

"We're very close to an FBI director," Trump said when asked about the search during an Oval Office appearance with Colombian President Juan Manuel Santos. Trump said "soon" when asked how close he is to making an announcement.

Trump leaves Friday afternoon on his first overseas trip as president, a four-country, five-stop tour that will keep him out of Washington for more than a week. He has said he could name a director before he departs.

The president also replied "he is" when asked whether Lieberman is a top candidate for the position.

Lieberman gave reporters a thumbs-up as he left the White House on Wednesday and said he and Trump had a "good meeting." Trump interviewed three other potential FBI director candidates the same day: former Oklahoma Gov. Frank Keating, former top FBI official Richard McFeely and Andrew McCabe. McCabe was tapped to become acting director after Trump dismissed Comey on May 9.

The firing was sharply criticized because it came amid the bureau's investigation into Russia's meddling in last year's presidential election.

"I cherish the FBI. It's special," Trump said later Thursday at a joint news conference with Santos. "All over the world, no matter where you go, the FBI is special." He said the bureau hasn't enjoyed "that special reputation" since during the presidential campaign.

Trump also criticized Comey for his performance during a recent appearance before Congress, and said Comey's replacement is "going to be outstanding."

Senate Republicans praised Lieberman, a Democrat turned independent, while Democrats were less effusive about their former colleague.

Sen. Lindsey Graham, R-S.C., called Lieberman a "pillar of credibility." Sen. John Cornyn of Texas, the No. 2 Republican in the Senate, said Lieberman "may be the only potential nominee that could get 100 votes that I know of. Everybody likes and respects Joe Lieberman."

But several Democratic senators said during a caucus lunch Thursday that they would not support Lieberman, according to a person familiar with the meeting who declined to be identified because the lunch was private.

Among their concerns was Lieberman's past praise of Michael Flynn, Trump's first national security adviser, who was fired in February after misleading officials about his conversations with Russian officials. Flynn has figured prominently in the FBI investigation into Russian interference into the election.

A Nov. 25 news release from Trump's transition team quoted Lieberman praising Trump's selection of K.T. McFarland as deputy national security adviser. Lieberman added that McFarland "and General Mike Flynn will form a very strong leadership team at the National Security Council."

Neera Tanden, president of the Center for American Progress, a Democratic think tank, also opposes Lieberman, saying he lacks law enforcement experience and is close to Attorney General Jeff Sessions, a former U.S. senator. Lieberman testified in support of Sessions at his January confirmation hearing.

Lieberman served in the Senate for more than two decades and was the Democratic vice presidential nominee in 2000 with Al Gore, then the sitting vice president. Lieberman lost his 2006 Democratic primary bid but won Senate re-election as a third-party candidate.

Lieberman spoke at the 2008 Republican National Convention on behalf of his friend, Arizona Sen. John McCain, and did not seek re-election in 2012. He has served as co-chairman of No Labels, a centrist group that promotes bipartisanship.

Keating, a Republican, was a two-term governor of Oklahoma and led the state during the deadly 1995 bombing of a federal building in Oklahoma City. A former FBI agent, Keating served in the administrations of Presidents Ronald Reagan and George H.W. Bush.

Keating told The Oklahoman he does not expect to be chosen.

"If they wanted me, I certainly would be honored, but I really don't think that's going to happen," he told the newspaper after his interview.

McCabe, a veteran FBI official, made headlines for congressional testimony last week that rejected White House claims that Comey had lost the support of rank-and-file agents. He also disputed the administration's characterization of the investigation into potential coordination between Russia and Trump associates.

Several candidates have withdrawn from consideration: Republican Rep. Trey Gowdy of South Carolina; Cornyn; Alice Fisher, the former head of the Justice Department's criminal division; and Michael Garcia, a former U.S. attorney from Manhattan.